Time Refraction and Time Reflection above Critical Angle for Total Internal Reflection

We study the time reflection and time refraction of waves caused by a spatial interface with a medium undergoing a sudden temporal change in permittivity. We show that monochromatic waves are transformed into a pulse by the permittivity change, and that time reflection is enhanced at the vicinity of the critical angle for total internal reflection. In this regime, we find that the evanescent field is transformed into a propagating pulse by the sudden change in permittivity. These effects display enhancement of the time reflection and high sensitivity near the critical angle, paving the way to experiments on time reflection and photonic time crystals at optical frequencies.